The Study Of Several Risk Models With Interference

Risk theory is an important branch of modern applied mathematics. In addition to theinsurance industry，it also mainly used in the field of finance, securities investment andrisk management. It constructed a mathematical model by means of probability theory andstochastic processes theory，the risk theory can be a tool for the operators or policymakersrisk quantitative to analyze and predict risk, it has been widely used in the investment andinsurance industries. The papers have discussed the probability of ruin of several modelsthat obey different distribution for the insurance company which is on the basis ofclassical risk model.Firstly, we have introduced some basic knowledge about this topic, such as theresearch methods and meaning of the risk theoretical, and the research directions and themain contents of this article.Secondly, when the mean equal to variance of the number of claims, we consider arisk model that obeys Poisson distribution with surrender confounding factors, we usesome methods such as the martingale model to obtain the bankruptcy probabilityexpressions and Lundberg upper bound. In order to make the model more in line with theactual development needs of the insurance company, we need consider the change of thelower limit of the risk model, and then we have obtained the similar conclusion.Again, when the average number of claims is less than the variance, then we considerthe negative binomial risk model with interference, and then we discuss the negativebinomial risk model with change of the lower limit, and we get the probability ofbankruptcy of the two model expressions and Lundberg upper bound.Finally, when the mean is greater than the variance of the number of claims, weconsider surrenders, claims interference factors and then change the lower limit of thebinomial model, lastly, we get the expressions of the model under bankruptcy probability.